/*******************************************************************************
*  Copyright (C) 2009-2015 Intel Corporation. All Rights Reserved.
*  The information and material ("Material") provided below is owned by Intel
*  Corporation or its suppliers or licensors, and title to such Material remains
*  with Intel Corporation or its suppliers or licensors. The Material contains
*  proprietary information of Intel or its suppliers and licensors. The Material
*  is protected by worldwide copyright laws and treaty provisions. No part of
*  the Material may be copied, reproduced, published, uploaded, posted,
*  transmitted, or distributed in any way without Intel's prior express written
*  permission. No license under any patent, copyright or other intellectual
*  property rights in the Material is granted to or conferred upon you, either
*  expressly, by implication, inducement, estoppel or otherwise. Any license
*  under such intellectual property rights must be express and approved by Intel
*  in writing.
*
********************************************************************************
*/
/*
   LAPACKE_zgesv Example.
   ======================

   The program computes the solution to the system of linear
   equations with a square matrix A and multiple
   right-hand sides B, where A is the coefficient matrix:

   (  1.23, -5.50) (  7.91, -5.38) ( -9.80, -4.86) ( -7.32,  7.57)
   ( -2.14, -1.12) ( -9.92, -0.79) ( -9.18, -1.12) (  1.37,  0.43)
   ( -4.30, -7.10) ( -6.47,  2.52) ( -6.51, -2.67) ( -5.86,  7.38)
   (  1.27,  7.29) (  8.90,  6.92) ( -8.82,  1.25) (  5.41,  5.37)

   and B is the right-hand side matrix:

   (  8.33, -7.32) ( -6.11, -3.81)
   ( -6.18, -4.80) (  0.14, -7.71)
   ( -5.71, -2.80) (  1.41,  3.40)
   ( -1.60,  3.08) (  8.54, -4.05)

   Description.
   ============

   The routine solves for X the system of linear equations A*X = B,
   where A is an n-by-n matrix, the columns of matrix B are individual
   right-hand sides, and the columns of X are the corresponding
   solutions.

   The LU decomposition with partial pivoting and row interchanges is
   used to factor A as A = P*L*U, where P is a permutation matrix, L
   is unit lower triangular, and U is upper triangular. The factored
   form of A is then used to solve the system of equations A*X = B.

   Example Program Results.
   ========================

 LAPACKE_zgesv (column-major, high-level) Example Program Results

 Solution
 ( -1.09, -0.18) (  1.28,  1.21)
 (  0.97,  0.52) ( -0.22, -0.97)
 ( -0.20,  0.19) (  0.53,  1.36)
 ( -0.59,  0.92) (  2.22, -1.00)

 Details of LU factorization
 ( -4.30, -7.10) ( -6.47,  2.52) ( -6.51, -2.67) ( -5.86,  7.38)
 (  0.49,  0.47) ( 12.26, -3.57) ( -7.87, -0.49) ( -0.98,  6.71)
 (  0.25, -0.15) ( -0.60, -0.37) (-11.70, -4.64) ( -1.35,  1.38)
 ( -0.83, -0.32) (  0.05,  0.58) (  0.93, -0.50) (  2.66,  7.86)

 Pivot indices
      3      3      3      4
*/
#include "mkl_lapacke.h"
#include <stdio.h>
#include <stdlib.h>

/* Auxiliary routines prototypes */
extern void print_matrix(char *desc, MKL_INT m, MKL_INT n, MKL_Complex16 *a,
                         MKL_INT lda);
extern void print_int_vector(char *desc, MKL_INT n, MKL_INT *a);

/* Parameters */
#define N 4
#define NRHS 2
#define LDA N
#define LDB N

/* Main program */
int main() {
  /* Locals */
  MKL_INT n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info;
  /* Local arrays */
  MKL_INT ipiv[N];
  MKL_Complex16 a[LDA * N] = {
      {1.23, -5.50},  {-2.14, -1.12}, {-4.30, -7.10}, {1.27, 7.29},
      {7.91, -5.38},  {-9.92, -0.79}, {-6.47, 2.52},  {8.90, 6.92},
      {-9.80, -4.86}, {-9.18, -1.12}, {-6.51, -2.67}, {-8.82, 1.25},
      {-7.32, 7.57},  {1.37, 0.43},   {-5.86, 7.38},  {5.41, 5.37}};
  MKL_Complex16 b[LDB * NRHS] = {{8.33, -7.32}, {-6.18, -4.80}, {-5.71, -2.80},
                                 {-1.60, 3.08}, {-6.11, -3.81}, {0.14, -7.71},
                                 {1.41, 3.40},  {8.54, -4.05}};
  /* Executable statements */
  printf("LAPACKE_zgesv (column-major, high-level) Example Program Results\n");
  /* Solve the equations A*X = B */
  info = LAPACKE_zgesv(LAPACK_COL_MAJOR, n, nrhs, a, lda, ipiv, b, ldb);
  /* Check for the exact singularity */
  if (info > 0) {
    printf("The diagonal element of the triangular factor of A,\n");
    printf("U(%i,%i) is zero, so that A is singular;\n", info, info);
    printf("the solution could not be computed.\n");
    exit(1);
  }
  /* Print solution */
  print_matrix("Solution", n, nrhs, b, ldb);
  /* Print details of LU factorization */
  print_matrix("Details of LU factorization", n, n, a, lda);
  /* Print pivot indices */
  print_int_vector("Pivot indices", n, ipiv);
  exit(0);
} /* End of LAPACKE_zgesv Example */

/* Auxiliary routine: printing a matrix */
void print_matrix(char *desc, MKL_INT m, MKL_INT n, MKL_Complex16 *a,
                  MKL_INT lda) {
  MKL_INT i, j;
  printf("\n %s\n", desc);
  for (i = 0; i < m; i++) {
    for (j = 0; j < n; j++)
      printf(" (%6.2f,%6.2f)", a[i + j * lda].real, a[i + j * lda].imag);
    printf("\n");
  }
}

/* Auxiliary routine: printing a vector of integers */
void print_int_vector(char *desc, MKL_INT n, MKL_INT *a) {
  MKL_INT j;
  printf("\n %s\n", desc);
  for (j = 0; j < n; j++)
    printf(" %6i", a[j]);
  printf("\n");
}
